Fractions - Addition & Subtraction

In this article, we will learn more about Addition and Subtraction of Fractions in \(\text{P5}\) level.  We will also be solving simple word problems involving addition and subtraction.

The learning objectives are:

1. Relating fractions and division
2. Addition of mixed numbers 
3. Subtraction of mixed numbers 
4. Simple word problems involving addition and subtraction of mixed numbers

1. Relating Fractions And Division

Fraction is related to division. 

\(\begin{align*} \frac {1} {3} \end{align*}\) is the same as \(\begin{align*} 1 \div 3 \end{align*}\).

Question 1: 

Express each of the following as a fraction. 

A. \(3 \div 5 =\text{__________}\)

B. \(5 \div 9 = \text{__________}\)

C. \(6 \div 11 = \text{__________}\)

Solution: 

A. \(\displaystyle{3 \div 5 =\frac {3}{5}}\)

B. \(\displaystyle{5 \div 9 = \frac {5}{9}}\)

C. \(\displaystyle{ 6 \div 11 = \frac {6}{11} }\)

Question 2: 

Mary bought \(2\) pies. She divided it equally among her \(3\) children. What fraction of a pie did each child receive?

Solution: 

Fraction of a pie each child received  \(\displaystyle{=2 \div 3\\[2ex] = \frac {2}{3} }\)

Answer:

\(\begin{align*} \frac {2}{3} \end{align*}\)

Question 3:

Jack baked \(15\) muffins and shared them equally with \(6\) friends. What fraction of the muffins did each of them receive?

Solution: 

Total muffins baked \(= 15\) muffins

Total number of friends including Jack \(= 7\)

15 muffins are shared \(\text{equally}\) among \(7 \text{ people}\).

Method 1:

Fraction of muffins received by each friend \(\displaystyle{= 15 \div 7\\[2ex] = \frac{15}{7}\\[3ex] = 2\frac{1}{7}\\[3ex]}\)        

Method 2:

\(\require{enclose} \begin{array}{rll} 0 \;2\phantom{000} \\[-3pt] 7\; \enclose{longdiv}{1\;5\quad}\kern-.3ex \\[-3pt] \underline{^-0\phantom{000}} \\[-3pt] 1\;5 \phantom{00} \\[-3pt] \underline{^-\text{1 4}\quad}\phantom{} \\[-3pt] 1 \phantom{00} \\[-3pt] \end{array}\)

Answer:

\(\begin{align*} 2 \frac {1}{7} \end{align*}\)

2. Addition Of Mixed Numbers 

To do addition of mixed numbers, we do the following steps:

Step 1:

Add the whole numbers.

Step 2:

Ensure that the denominators are the same. Make the denominators the same if they are not.

Step 3:

Add the fractions. 

Step 4:

Simplify and express as a mixed number if possible. 

Question 1: 

Add the following.

\(\begin{align*} 2\frac { 2} { 5} + 5\frac {1 } {5 } \end{align*}\)

Solution: 

\(\begin{align*} 2\frac { 2} { 5} + 5\frac {1 } {5 } &= 7\frac { 2} { 5} + \frac {1 } {5 }\\ \\ &= 7\frac { 3} { 5} \\ \end{align*}\)

Question 2: 

Add the following.

\(\begin{align*} 1\frac {7} {10} + 6\frac {9} {10} \end{align*}\)

Solution: 

\(\begin{align*} 1\frac { 7} { 10} + 6\frac {9 } {10 } &= 7\frac { 7} { 10} + \frac {9 } {10 }\\ \\ &= 7\frac { 16} { 10} \\ \\ &= 8\frac { 6} { 10} \\ \\ &= 8\frac { 3} { 5} \\ \end{align*}\)

Answer:

\(\begin{align*} 8\frac { 3} { 5} \end{align*}\)

Question 3: 

Add the following.

\(\begin{align*} 2\frac {3} {4} + 3\frac {5} {6} \end{align*}\)

Solution: 

\(\begin{align*} 2\frac { 3} { 4} + 3\frac {5 } {6} &= 5\frac { 3} { 4} + \frac {5 } {6 }\\ \\ &= 5\frac { 9} { 12} + \frac {10 } {12 }\\ \\ &= 5\frac { 19} { 12} \\ \\ &= 6\frac { 7} { 12} \\ \end{align*} \)
 

Answer:

\(\begin{align*} 6\frac { 7} { 12} \end{align*}\)

Question 4: 

Add the following.

\(\begin{align*} 1\frac {6} {7} + 5\frac {9} {14} \end{align*}\)

Solution: 

\(\begin{align*} 1\frac { 6} { 7} + 5\frac {9 } {14} &= 6\frac { 6} { 7} + \frac {9 } {14 }\\ \\ &= 6\frac { 12} { 14} + \frac { 9} { 14}\\ \\ &= 6\frac { 21} { 14} \\ \\ &= 7\frac { 7} { 14} \\ \\ &= 7\frac { 1} { 2} \\ \end{align*}\)

Answer:

\(\begin{align*} 7\frac { 1} { 2} \end{align*}\)

3. Subtraction Of Mixed Numbers

To do addition of mixed numbers, we do the following steps:

Step 1:

Subtract the whole numbers.

Step 2:

Ensure that the denominators are the same. Make the denominators the same if they are not.

Step 3:

Rename the first mixed number if the numerators cannot be subtracted.

Step 4:

Subtract the fractions.

Step 5:

Simplify and express as a mixed number if possible.

Question 1: 

Subtract the following. 

\(\begin{align*} 5\frac {5} {6} - 1\frac {1} {3} \end{align*}\)

Solution: 

\(\begin{align*} 5\frac {5} {6} - 1\frac {1} {3} &= 4\frac { 5} { 6} - \frac {1 } {3 }\\ \\ &= 4\frac { 5} { 6} - \frac {2 } {6 }\\ \\ &= 4\frac { 3} { 6} \\ \\ &= 4\frac { 1} { 2} \\ \end{align*}\)

Answer:

\(\begin{align*} 4\frac { 1} { 2} \end{align*}\)

Question 2: 

Subtract the following.

\(\begin{align*} 7\frac {3} {8} - 6\frac {7} {8} \end{align*}\)

Solution: 

\(\begin{align*} 7\frac {3} {8} - 6\frac {7} {8} &= 1\frac { 3} { 8} - \frac {7 } {8 }\\ \\ &= \frac { 11} { 8} - \frac {7 } {8 }\\ \\ &= \frac { 4} { 8} \\ \\ &= \frac { 1} { 2} \\ \end{align*}\)

Alternatively, convert both fractions to improper fractions.

\(\begin{align*} 7\frac {3} {8} - 6\frac {7} {8} &= \frac { 59} { 8} - \frac {55} {8 }\\ \\ &= \frac { 4} { 8} \\ \\ &= \frac { 1} { 2} \\ \end{align*}\)

Answer:

\(\begin{align*} \frac {1} {2} \end{align*}\)

Question 3: 

Subtract the following.

\(\begin{align*} 6\frac {3} {10} - 1\frac {1} {2} \end{align*}\)

Solution: 

\(\begin{align*} 6\frac {3} {10} - 1\frac {1} {2} &= 5\frac { 3} { 10} - \frac {1} {2}\\ \\ &= 5\frac { 3} { 10} - \frac {5} {10} \\ \\ &= 4\frac { 13} { 10} - \frac {5} {10} \\ \\ &= 4\frac { 8} { 10} \\ \\ &= 4\frac { 4} { 5} \\ \end{align*}\)

Alternatively, convert both fractions to improper fractions.

\(\begin{align*} 6\frac {3} {10} - 1\frac {1} {2} &= \frac { 63} { 10} - \frac {3} {2} \\[3ex] &= \frac { 63} { 10} - \frac {15} {10} \\[3ex] &= \frac {48} { 10} \\[3ex] &= 4\frac { 8} { 10} \\[3ex] &= 4\frac { 4} { 5} \end{align*}\)

Answer:

\(\begin{align*} 4\frac { 4} { 5} \end{align*}\)

Question 4: 

Subtract the following.

\(\begin{align*} 5\frac {7} {10} - 3\frac {3} {4} \end{align*}\)

Solution: 

\(\begin{align*} 5\frac { 7 } { 10 } - 3 \frac { 3 } { 4 } &= 2 \frac { 7 } { 10 } - \frac { 3 } { 4 }\\ \\ &= 2 \frac { 14 } { 20 } - \frac { 15 } { 10 } \\ \\ &= 1 \frac { 34 } { 20 } - \frac { 15 } { 10 }\\ \\ &= 1\frac { 19 } { 20 } \\ \end{align*}\)

Answer:

\(\begin{align*} 1\frac { 19 } { 20 } \end{align*}\)

4. Word Problems Involving Addition And/or Subtraction Of Mixed Numbers

Question 1: 

Jane had \(\begin{align*} 2\frac { 3 } { 5 }\; \text {kg} \end{align*}\) of coffee powder. Sarah has \(\begin{align*} 1\frac { 1 } { 5 } \; \text {kg} \end{align*}\) of coffee powder more than Jane. How much coffee powder does Sarah have?

Solution: 

Mass of coffee powder Sarah has \(\displaystyle{= 2 \frac { 3 } { 5 } \; \text {kg} + 1\frac { 1 } { 5 } \;\text {kg}\\[3ex] = 3 \frac { 4 } { 5 } \; \text {kg}}\)

Answer:

\(\begin{align*} 3 \frac { 4 } { 5 } \; \text {kg} \end{align*}\)

Question 2: 

Mrs Tan had \(\begin{align*} 5\frac { 1 } { 2 }\; \text {kg} \end{align*}\) of flour. She had \(\begin{align*} 2\frac { 5 } { 6 }\; \text {kg} \end{align*}\) of flour more than Mrs Loh. How much flour did they have altogether?

Solution: 

Mass of flour Mrs Loh had \(\displaystyle{= 5\frac { 1 } { 2 }\; \text {kg} - 2\frac { 5 } { 6 }\; \text {kg}\\[3ex] = 3\frac { 1 } { 2 }\; \text {kg} - \frac { 5 } { 6 }\; \text {kg} \\[3ex] = 3\frac { 3 } { 6 }\; \text {kg} - \frac { 5 } { 6 }\; \text {kg} \\[3ex] = 2\frac { 9 } { 6 }\; \text {kg} - \frac { 5 } { 6 }\; \text {kg} \\[3ex] = 2\frac { 4 } { 6 }\; \text {kg} \\[3ex] = 2\frac { 2 } { 3 }\; \text {kg}}\)  

Total mass of flour they had \(\displaystyle{= 5\frac { 1 } { 2 }\; \text {kg} + 2\frac { 2 } { 3 }\; \text {kg} \\[3ex] = 7\frac { 1 } { 2 }\; \text {kg} + \frac { 2 } { 3 }\; \text {kg} \\[3ex] = 7\frac { 3 } { 6 }\; \text {kg} + \frac { 4 } { 6 }\; \text {kg} \\[3ex] = 7\frac { 7 } { 6 }\; \text {kg} \\[3ex] = 8\frac { 1 } { 6 }\; \text {kg}}\)

Answer:

\(\begin{align*} 8\frac { 1 } { 6 }\; \text {kg} \end{align*}\)

Question 3:

Sandy had \(\begin{align*} 3\frac { 1 } { 2 }\; \text {kg} \end{align*}\) of sugar. She had \(\begin{align*} 2\frac { 5 } { 6 }\; \text {kg} \end{align*}\) of sugar less than Amy. How many kilograms of sugar did they have altogether?

Solution: 

Mass of sugar Amy had \(\displaystyle{= 3\frac { 1 } { 2 }\; \text {kg} + 2\frac { 5 } { 6 }\; \text {kg} \\[3ex] = 5\frac { 1 } { 2 }\; \text {kg} + \frac { 5 } { 6 }\; \text {kg} \\[3ex] = 5\frac { 3 } { 6 }\; \text {kg} + \frac { 5 } { 6 }\; \text {kg} \\[3ex] = 5\frac { 8 } { 6 }\; \text {kg} \\[3ex] = 6\frac { 2 } { 6 }\; \text {kg} \\[3ex] = 6\frac { 1 } { 3 }\; \text {kg}}\)

Total mass of sugar Sandy and Amy had \(\displaystyle{= 3\frac { 1 } { 2 }\; \text {kg} + 6\frac { 1 } { 3 }\; \text {kg} \\[3ex] = 9\frac { 1 } { 2 }\; \text {kg} + \frac { 1 } { 3 }\; \text {kg} \\[3ex] = 9\frac { 3 } { 6 }\; \text {kg} + \frac { 2 } { 6 }\; \text {kg} \\[3ex] = 9\frac { 5 } { 6 }\; \text {kg}}\)

Answer:

\(\begin{align*} 9\frac { 5 } { 6 }\; \text {kg} \end{align*}\)

Conclusion

In this article, we have learnt about Addition and Subtraction of Fractions as per the Primary 5 Math level. We have learnt the following subtopics in fractions.

• Relating fractions and division
• Addition of mixed numbers 
• Subtraction of mixed numbers 
• Simple word problems involving addition and subtraction of mixed numbers